Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

<image>

In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main {
    public static void main(String[] args) throws IOException{
        //BufferedReader f = new BufferedReader(new FileReader("uva.in"));
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        StringTokenizer st = new StringTokenizer(f.readLine());
        int n = Integer.parseInt(st.nextToken());
        int m = Integer.parseInt(st.nextToken());
        int[][] g = new int[n][m];
        for(int i = 0; i < n; i++) {
            st = new StringTokenizer(f.readLine());
            for(int j = 0; j < m; j++) {
                g[i][j] = Integer.parseInt(st.nextToken());
            }
        }
        if(n < m) {
            ArrayList<String> moves = new ArrayList<>();
            int min = 500;
            for(int i = 0; i < m; i++) {
                min = Math.min(min, g[0][i]);
            }
            for(int i = 0; i < min; i++) {
                moves.add("row 1");
            }
            boolean valid = true;
            for(int i = 0; i < m; i++) {
                g[0][i] -= min;
                if(g[0][i] > 0) {
                    for(int j = 1; j < n; j++) {
                        g[j][i] -= g[0][i];
                        if(g[j][i] < 0) {
                            valid = false;
                            break;
                        }
                    }
                    if(!valid) {
                        break;
                    }
                    for(int j = 0; j < g[0][i]; j++) {
                        moves.add("col " + (i+1));
                    }
                    g[0][i] = 0;
                }
            }
            if(valid) {
                for(int i = 1; i < n; i++) {
                    for(int j = 1; j < m; j++) {
                        g[i][j] -= g[i][0];
                        if(g[i][j] != 0) {
                            valid = false;
                            break;
                        }
                    }
                    if(!valid) {
                        break;
                    }
                    for(int j = 0; j < g[i][0]; j++) {
                        moves.add("row " + (i+1));
                    }
                    g[i][0] = 0;
                }
            }
            if(valid) {
                out.println(moves.size());
                for(String i: moves) {
                    out.println(i);
                }
            } else {
                out.println(-1);
            }
        } else {
            ArrayList<String> moves = new ArrayList<>();
            int min = 500;
            for(int i = 0; i < n; i++) {
                min = Math.min(min, g[i][0]);
            }
            for(int i = 0; i < min; i++) {
                moves.add("col 1");
            }
            boolean valid = true;
            for(int i = 0; i < n; i++) {
                g[i][0] -= min;
                if(g[i][0] > 0) {
                    for(int j = 1; j < m; j++) {
                        g[i][j] -= g[i][0];
                        if(g[i][j] < 0) {
                            valid = false;
                            break;
                        }
                    }
                    if(!valid) {
                        break;
                    }
                    for(int j = 0; j < g[i][0]; j++) {
                        moves.add("row " + (i+1));
                    }
                    g[i][0] = 0;
                }
            }
            if(valid) {
                for(int i = 1; i < m; i++) {
                    for(int j = 1; j < n; j++) {
                        g[j][i] -= g[0][i];
                        if(g[j][i] != 0) {
                            valid = false;
                            break;
                        }
                    }
                    if(!valid) {
                        break;
                    }
                    for(int j = 0; j < g[0][i]; j++) {
                        moves.add("col " + (i+1));
                    }
                    g[0][i] = 0;
                }
            }
            if(valid) {
                out.println(moves.size());
                for(String i: moves) {
                    out.println(i);
                }
            } else {
                out.println(-1);
            }
        }
        f.close();
        out.close();
    }
}